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If Google has said to look at their list then I would dig deep into that list.  It could be something other than a overly optimized anchor.  Check out the domains, pages links are placed.... are they selling links or up to something sketchy?

We handle resort/hotel sites with different engines,  From a link and ranking standpoint in the travel space I don't see a benefit to use the engine content/links to help you rank.

Sure you can pop some links in there but nothing that will let you compete in Travel.  Yes you will get some inbound links but not quality links and a lot of engine stuff does not get indexed.

Then you are looking at duplicate content as well across all sites using the engine, this can be a crusher for you.

IMO the only purpose of the engine is to take the user through the booking process period. (and that is a science in itself to get people to convert)

In your theme goto graysclae/template/page/html/head.phtml

This line adds your site name in

<title>echo $this->getTitle() ?>title>

He has the basics covered,  is using the keyword 1st in Title,Desc.   On page he leads the H1 with the keyword, uses it in the body and as a link.  Position 2 & 3 do not have these all together.  Plus Pos 2 & 3 using as external site wide anchors which is probably hurting them the most.

In your theme goto graysclae/template/page/html/head.phtml

This line adds your site name in

<title>echo $this->getTitle() ?>title>